document.write( "Question 114077: Will donate. Please help solve two problems.
\n" ); document.write( "1.Use the properties of logarithms to write the following expression as a single logarithm:
\n" ); document.write( "\"2%2Alog%28x%29%2B2%2Alog%28y%29-4%2Alog%28z%29\"
\n" ); document.write( "2.Use the properties of logarithms to expand the expression as much as possible:
\n" ); document.write( "\"+log+%283%2C+%2881z%2Fy%5E3x%5E4%29%29+\"
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Algebra.Com's Answer #83034 by Edwin McCravy(20059)\"\" \"About 
You can put this solution on YOUR website!
Will donate. Please help solve two problems.
\n" ); document.write( "1.Use the properties of logarithms to write the following expression as a single logarithm:
\n" ); document.write( "\"2%2Alog%28x%29%2B2%2Alog%28y%29-4%2Alog%28z%29\"
\n" ); document.write( "2.Use the properties of logarithms to expand the expression as much as possible:
\n" ); document.write( "\"+log+%283%2C+%2881z%2Fy%5E3x%5E4%29%29+\"
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document.write( "Here are the properties of logarithms we need. Notice that\r\n" );
document.write( "the \"A\" and \"B\" properties are the same except that the\r\n" );
document.write( "left and right sides are switched. We need the \"B\" properties\r\n" );
document.write( "to write as a single logarithm, and the \"A\" properties to expand\r\n" );
document.write( "a logarithm expression:\r\n" );
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document.write( "Property 1A: \"log%28b%2C%28FIRST%2ASECOND%29%29=log%28b%2C%28FIRST%29%29%2Blog%28b%2C%28SECOND%29%29+%29\"\r\n" );
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document.write( "Property 1B: \"log%28b%2C%28FIRST%29%29%2Blog%28b%2C%28SECOND%29%29=log%28b%2C%28FIRST%2ASECOND%29%29\"\r\n" );
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document.write( "Property 2A: \r\n" );
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document.write( "Property 2B: \r\n" );
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document.write( "Property 3A: \"log%28b%2C%28EXPRESSION%29%5E%28EXPONENT%29%29=EXPONENT%2Alog%28b%2C%28EXPRESSION%29%29+\"\r\n" );
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document.write( "Property 3B: \r\n" );
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document.write( "Property 4: \"log%28b%2C%28b%5E%28EXPONENT%29%29%29=EXPONENT\"\r\n" );
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document.write( "-----------------------------------------------------\r\n" );
document.write( "1.Use the properties of logarithms to write the following\r\n" );
document.write( "  expression as a single logarithm:\r\n" );
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document.write( " \"2%2Alog%28x%29%2B2%2Alog%28y%29-4%2Alog%28z%29\" \r\n" );
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document.write( "Use Property 3B on each of the three terms:\r\n" );
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document.write( "\"log%28x%5E2%29%2Blog%28y%5E2%29-log%28z%5E4%29\"\r\n" );
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document.write( "Use Property 1B on the first two terms:\r\n" );
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document.write( "\"log%28x%5E2y%5E2%29-log%28z%5E4%29\"\r\n" );
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document.write( "Use Property 2B on that\r\n" );
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document.write( "\"log%28%28%28x%5E2y%5E2%29%2F%28z%5E4%29%29%29\"\r\n" );
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document.write( "That is a single logarithm.\r\n" );
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document.write( "----------------------------------------\r\n" );
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document.write( "2.Use the properties of logarithms to expand the expression as much as possible: \r\n" );
document.write( "\r\n" );
document.write( "\"+log+%283%2C+%2881z%2F%28y%5E3x%5E4%29%29%29+\"\r\n" );
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document.write( "Use Property 2:\r\n" );
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document.write( "\"log%283%2C%2881z%29%29-log%283%2C%28y%5E3x%5E4%29%29+%29\"\r\n" );
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document.write( "Use Property 1 on both terms, but be\r\n" );
document.write( "sure to enclose the 2nd in parentheses\r\n" );
document.write( "since it is preceded by a minus sign:\r\n" );
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document.write( "\"log%283%2C81%29%2Blog%283%2Cz%29-%28log%283%2Cy%5E3%29%2Blog%283%2Cx%5E4%29%29+%29\"\r\n" );
document.write( "Remove the parentheses:\r\n" );
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document.write( "\"log%283%2C81%29%2Blog%283%2Cz%29-log%283%2Cy%5E3%29-log%283%2Cx%5E4%29%29+\"\r\n" );
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document.write( "Use Property 3 on the third and fourth terms:\r\n" );
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document.write( "\"log%283%2C81%29%2Blog%283%2Cz%29-3%2Alog%283%2Cy%29-4%2Alog%283%2Cx%29%29+\"\r\n" );
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document.write( "Write \"81\" as \"3%5E4\"\r\n" );
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document.write( "\"log%283%2C3%5E4%29%2Blog%283%2Cz%29-3%2Alog%283%2Cy%29-4%2Alog%283%2Cx%29%29+\"\r\n" );
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document.write( "Use Property 4 on the first term\r\n" );
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document.write( "\"4%2Blog%283%2Cz%29-3%2Alog%283%2Cy%29-4%2Alog%283%2Cx%29%29+\"\r\n" );
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document.write( "That's as far as it will expand.\r\n" );
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document.write( "Edwin
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